An energy basis for mesh refinement of structural continua

Melosh, R. J.; Marcal, Pedro V.

doi:10.1002/nme.1620110705

Cited by 76 publications

(13 citation statements)

References 1 publication

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“…Using group theory, Punch 55] used orthogonal lower-and higher-order stress modes to construct hybrid element. It allows the partition of the element stiffness matrix into a lower-and a higher-order stiffness matrix.…”

Section: Approaches To Obtain An Assumed Stress Fieldmentioning

confidence: 99%

Hybrid Finite Element Method for Stress Analysis of Laminated Composites

Hoa

Feng

1998

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Section: Approaches To Obtain An Assumed Stress Fieldmentioning

confidence: 99%

Hybrid Finite Element Method for Stress Analysis of Laminated Composites

Hoa

Feng

1998

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“…To determine which portions of the mesh required refinement or optimization, the differences between the strain energy densities at neighboring Gaussian quadrature integration points within each element and across each interelement boundary were computed. A large difference indicates departure from constant strain conditions and suggests the need for mesh refinement [50,77]. The positions of the element boundaries were adjusted until these strain energy density differences were less than 10% throughout the longitude.…”

Section: An Axisymmetric Finite Element Model Of the Passive Left Venmentioning

confidence: 99%

Finite Element Modeling of Ventricular Mechanics

Guccione

McCulloch

1991

Institute for Nonlinear Science

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Computing the distributions of stress and strain in a body with the complex geometry, boundary conditions, and material properties of the heart is a difficult yet worthwhile endeavor. The most promising method for obtaining numerical solutions to this problem is the finite element method. In this chapter, we review the use of finite element analysis for modeling ventricular mechanics. And we conclude by presenting a new axisymmetric finite element model of the passive left ventricle with a realistic geometry and fibrous architecture, physiological boundary conditions, and a three-dimensional constitutive equation. IntroductionThe distributions of stress in the ventricles of the heart are determined by (1) the three-dimensional geometry and fibrous architecture of the ventricular walls, (2) the boundary conditions imposed by the ventricular cavity and pericardial pressures and structures like the fibrous valve ring skeleton at the base of the ventricles, and (3) the three-dimensional mechanical properties of the myofibers and their collagen interconnections in the relaxed and actively contracting states. Many of these determining factors have been quantified in experimental studies, some of which are described in detail in this book.For example, Streeter and Hanna [72,73] and Nielsen and coworkers [56] have made detailed studies of the three-dimensional geometry and myocardial fiber architecture of the ventricles of the dog heart. Measurements of left and right ventricular pressures in patients are quite routine. And extensive data have been collected on the passive and active uniaxial material properties of isolated papillary muscles and trabeculae from various mammalian species [64,74]. Although fully triaxial material testing still presents significant technical difficulties, biaxial stress-strain testing of excised two-

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“…This can be avoided if new subelements are created keeping the original shape of the element as shown in Fig. 6c [21][22][23][24][25]. This approach to element refinement will require the use of constraint equations for the new midedge nodes introduced along the original element edge.…”

Section: Mesh Updatingmentioning

confidence: 99%

Adaptive multiple-levelh-refinement in automated finite element analyses

Baehmann

Shephard

1989

Engineering with Computers

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Abstract. This paper discusses an automatic, adaptive finite element modeling system consisting of mesh generation, finite element analysis, and error estimation. The individual components interact with one another and efficiently reduce the finite element error to within an acceptable value and perform only a minimum number of finite element analyses.One of the necessary.components in the automated system is a multiple-level local remeshing algorithm. Given h-refinement information provided by an a posteriori error estimator, and adjacency information available in the mesh data structures, the local remeshing algorithm grades the refinement toward areas requesting refinement. It is shown that the optimal asymptotic convergence rate is achieved, demonstrating the effectiveness of the intelligent multiple-level local h-refinement.

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An energy basis for mesh refinement of structural continua

Cited by 76 publications

References 1 publication

Hybrid Finite Element Method for Stress Analysis of Laminated Composites

Hybrid Finite Element Method for Stress Analysis of Laminated Composites

Finite Element Modeling of Ventricular Mechanics

Adaptive multiple-levelh-refinement in automated finite element analyses

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